The mass of a box measured by a grocer’s balance is 2.30 kg. Two gold pieces ofmasses 20.15 g and 20.17 g are added to the box. What is (a) the total mass of thebox, (b) the difference in the masses of the pieces to correct significant figures ?

(a) To find the total mass of the box, we first need to convert the masses of the gold pieces from grams to kilograms, since the mass of the box is given in kilograms.

1 kg = 1000 g

So, 20.15 g = 20.15/1000 kg = 0.02015 kg And, 20.17 g = 20.17/1000 kg = 0.02017 kg

Now, we add the masses:

Total mass = mass of box + mass of first gold piece + mass of second gold piece Total mass = 2.30 kg + 0.02015 kg + 0.02017 kg = 2.34032 kg

However, we should report our answer with the correct number of significant figures. The number with the least number of decimal places is 2.30 kg, which has two decimal places. So, our final answer should also have two decimal places.

Total mass = 2.34 kg

(b) To find the difference in the masses of the pieces, we subtract the smaller mass from the larger mass:

Difference = 20.17 g - 20.15 g = 0.02 g

Again, we should report our answer with the correct number of significant figures. Both 20.17 g and 20.15 g have four significant figures, so our final answer should also have four significant figures.

Difference = 0.02 g